Finite Group Databasebeta

← C13×#9998 #15696337

Subgroups — C13×#9998 #15696337

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3103C211yesmaximal, characteristic, complemented
2C13×#3036C211yesmaximal, characteristic
3C13×#2580C211yesmaximal, characteristic, complemented
4C13×#1517C211yesmaximal, characteristic, complemented
5C13×#1487C211yesmaximal, characteristic, complemented
6C13×#1478C211yesmaximal, characteristic, complemented
7C13×#1286C211yesmaximal, characteristic, complemented
8C2×C13×AGL(1,ℤ/8)—21no—
9C13×#532C2211yescharacteristic
10C2×C4×Q8×C13C2211yescharacteristic
11C2×C4×D4×C13C2211yescharacteristic
12C13×#481—21no—
13C13×#475—21no—
14C13×#463—22no—
15C13×#461—21no—
16C13×#460—21no—
17C13×#459—21no—
18C13×#448—21no—
19C4×C13×SD16—22no—
20C13×#431C2211yescharacteristic
21C13×#431C2211yescharacteristic
22C13×#423C2211yescharacteristic
23C13×#417—21no—
24C13×#399—21no—
25C13×#393—21no—
26C13×#390—21no—
27C13×#389—21no—
28C13×#385—22no—
29C13×#382C2211yescharacteristic
30C13×#327—22no—
31C13×Q8⋊C8—22no—
32C13×D4⋊C8—22no—
33C2×C13×#41—21no—
34C22×Q8×C13D411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C23×C4×C13—21no—
37C13×AGL(1,ℤ/8)—42no—
38C13×AGL(1,ℤ/8)—42no—
39C2×C13×SD16—22no—
40C2×C13×SD16—22no—
41C2×C13×D8—22no—
42C2×C13×M16—21no—
43C13×C4⋊Q8D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#124—21no—
46C13×#121—21no—
47C13×#121—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4D411yescharacteristic
62C2×C13×C4⋊C4D411yescharacteristic
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—22no—
66C2×C42×C13—21no—
67C2×C42×C13C2311yescharacteristic
68C13×#106—22no—
69C13×C4⋊C8—21no—
70C13×C4⋊C8—21no—
71C13×C4⋊C8—21no—
72C13×C4⋊C8D412yes—
73C13×#103—22no—
74C13×#103—22no—
75C13×#102—22no—
76C13×#102—22no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C4×C8×C13—21no—
80C4×C8×C13D412yes—
81C13×#95—22no—
82C13×#95—21no—
83C13×#95D412yes—
84#9998C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C13×#41—41no—
87C13×#41—41no—
88C13×#41—41no—
89C13×#41—41no—
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—21no—
93C2×Q8×C13—42no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—21no—
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13—21no—
101C2×D4×C13—21no—
102C2×D4×C13—41no—
103C2×D4×C13SD1612yescomplemented
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13—82no—
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C13×SD16—44no—
116C13×SD16—44no—
117C13×D8—44no—
118C13×M16—41no—
119C13×M16—41no—
120C2×C8×C13—22no—
121C2×C8×C13—22no—
122C2×C8×C13—41no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—41no—
130C13×C4⋊C4—41no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—82no—
134C13×C22⋊C4—44no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—82no—
140C42×C13—41no—
141C42×C13—41no—
142C42×C13C2×D411yescharacteristic
143C42×C13C2×D411yescharacteristic
144C42×C13C2×D411yescharacteristic
145C42×C13#4111yescharacteristic
146#3103C2×C1311yescharacteristic, complemented
147#3036C2×C1311yescharacteristic
148#2580C2×C1311yescharacteristic, complemented
149#1517C2×C1311yescharacteristic, complemented
150#1487C2×C1311yescharacteristic, complemented
151#1478C2×C1311yescharacteristic, complemented
152#1286C2×C1311yescharacteristic, complemented
153C23×C13—22no—
154C23×C13—42no—
155C23×C13—42no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13#12011yescharacteristic
160Q8×C13—22no—
161Q8×C13—22no—
162Q8×C13—41no—
163Q8×C13—41no—
164Q8×C13—41no—
165Q8×C13—41no—
166D4×C13—22no—
167D4×C13—22no—
168D4×C13—42no—
169D4×C13—41no—
170D4×C13—41no—
171D4×C13—41no—
172D4×C13—41no—
173D4×C13—81no—
174D4×C13—81no—
175D4×C13—81no—
176C2×C4×C13—22no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13—42no—
184C2×C4×C13—41no—
185C2×C4×C13—42no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—42no—
190C2×C4×C13—82no—
191C2×C4×C13—82no—
192C2×C4×C13—81no—
193C2×C4×C13—81no—
194C2×C4×C13#12011yescharacteristic
195C2×C4×C13#12011yescharacteristic
196C2×C4×C13#12111yescharacteristic
197C2×C4×C13#12111yescharacteristic
198C2×C4×C13#12111yescharacteristic
199C2×C4×C13#12711yescharacteristic
200C2×C4×C13C2×SD1611yescharacteristic
201C2×C4×C13#13511yescharacteristic
202C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C13#13711yescharacteristic
204C8×C13—42no—
205C8×C13—42no—
206C8×C13—81no—
207C2×AGL(1,ℤ/8)—21no—
208#532C22×C1311yescharacteristic
209C2×C4×Q8C22×C1311yescharacteristic
210C2×C4×D4C22×C1311yescharacteristic
211#481—21no—
212#475—21no—
213#463—22no—
214#461—21no—
215#460—21no—
216#459—21no—
217#448—21no—
218C4×SD16—22no—
219#431C22×C1311yescharacteristic
220#431C22×C1311yescharacteristic
221#423C22×C1311yescharacteristic
222#417—21no—
223#399—21no—
224#393—21no—
225#390—21no—
226#389—21no—
227#385—22no—
228#382C22×C1311yescharacteristic
229#327—22no—
230Q8⋊C8—22no—
231D4⋊C8—22no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—44no—
235C22×C13—42no—
236C22×C13—82no—
237C22×C13—81no—
238C22×C13—81no—
239C22×C13—81no—
240C22×C13—81no—
241C22×C13—81no—
242C22×C13#39211yescharacteristic
243C22×C13#44811yescharacteristic
244C22×C13#44911yescharacteristic
245C4×C13—21no—
246C4×C13—21no—
247C4×C13—21no—
248C4×C13—21no—
249C4×C13—42no—
250C4×C13—82no—
251C4×C13—81no—
252C4×C13—81no—
253C4×C13—81no—
254C4×C13#45011yescharacteristic
255C4×C13#45211yescharacteristic
256C4×C13#46511yescharacteristic
257C4×C13#46811yescharacteristic
258C2×#41—21no—
259C22×Q8D4×C1311yescharacteristic
260C22×D4D4×C1311yescharacteristic
261C23×C4—21no—
262AGL(1,ℤ/8)—42no—
263AGL(1,ℤ/8)—42no—
264C2×SD16—22no—
265C2×SD16—22no—
266C2×D8—22no—
267C2×M16—21no—
268C4⋊Q8D4×C1311yescharacteristic
269#127D4×C1311yescharacteristic
270#124—21no—
271#121—21no—
272#121—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4D4×C1311yescharacteristic
287C2×C4⋊C4D4×C1311yescharacteristic
288C2×C22⋊C4—22no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—22no—
291C2×C42—21no—
292C2×C42C23×C1311yescharacteristic
293#106—22no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8D4×C1312yes—
298#103—22no—
299#103—22no—
300#102—22no—
301#102—22no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C4×C8—21no—
305C4×C8D4×C1312yes—
306#95—22no—
307#95—21no—
308#95D4×C1312yes—
309C2×C13—21no—
310C2×C13—21no—
311C2×C13—82no—
312C2×C13—161no—
313C2×C13#200011yescharacteristic
314C2×C13#200811yescharacteristic
315C2×C13#201011yescharacteristic
316C24—21no—
317#41—41no—
318#41—41no—
319#41—41no—
320#41—41no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—42no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—41no—
334C2×D4C13×SD1612yescomplemented
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—82no—
343C22×C4C2×D4×C1311yescharacteristic
344C22×C4C2×D4×C1311yescharacteristic
345C22×C4C2×D4×C1311yescharacteristic
346SD16—44no—
347SD16—44no—
348D8—44no—
349M16—41no—
350M16—41no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—41no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—82no—
365C22⋊C4—44no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—82no—
371C42—41no—
372C42—41no—
373C42C2×D4×C1311yescharacteristic
374C42C2×D4×C1311yescharacteristic
375C42C2×D4×C1311yescharacteristic
376C42C13×#4111yescharacteristic
377C13#999811yescharacteristic, direct product factor, Sylow
378C23—22no—
379C23—42no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23C13×#12011yescharacteristic
385Q8—22no—
386Q8—22no—
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—41no—
391D4—22no—
392D4—22no—
393D4—42no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—81no—
399D4—81no—
400D4—81no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4C13×#12011yescharacteristic
420C2×C4C13×#12011yescharacteristic
421C2×C4C13×#12111yescharacteristic
422C2×C4C13×#12111yescharacteristic
423C2×C4C13×#12111yescharacteristic
424C2×C4C13×#12711yescharacteristic
425C2×C4C2×C13×SD1611yescharacteristic
426C2×C4C13×#13511yescharacteristic
427C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
428C2×C4C13×#13711yescharacteristic
429C8—42no—
430C8—42no—
431C8—81no—
432C22—21no—
433C22—21no—
434C22—44no—
435C22—42no—
436C22—82no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22C13×#39211yescharacteristic
443C22C13×#44811yescharacteristic
444C22C13×#44911yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4C13×#45011yescharacteristic
455C4C13×#45211yescharacteristic
456C4C13×#46511yescharacteristic
457C4C13×#46811yescharacteristic
458C2—21no—
459C2—21no—
460C2—82no—
461C2—161no—
462C2C13×#200011yescharacteristic
463C2C13×#200811yescharacteristic
464C2C13×#201011yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3036C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C13×#3103C2semidirect
3. C13×#2580C2semidirect
4. C13×#1517C2semidirect
5. C13×#1487C2semidirect
6. C13×#1478C2semidirect
7. C13×#1286C2semidirect
84. #9998C13direct (N × H)
103. C2×D4×C13SD16semidirect
146. #3103C2×C13semidirect
148. #2580C2×C13semidirect
149. #1517C2×C13semidirect
150. #1487C2×C13semidirect
151. #1478C2×C13semidirect
152. #1286C2×C13semidirect
334. C2×D4C13×SD16semidirect
377. C13#9998direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#31032
C13×#30362
C13×#25802
C13×#15172
C13×#14872
C13×#14782
C13×#12862
#999813